Academic Research Publishing Agency Press
International Journal of Research and Reviews in Applied Sciences
ISSN: 2076-734X, EISSN: 2076-7366

Volume 6, Issue 3 (February, 2011)
Special Issue on "Science and Mathematics with Applications"

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1. ON SOME FRACTIONAL PARABOLIC EQUATIONS DRIVEN BY FRACTIONAL GAUSSIAN NOISE
by Mahmoud M. El-Borai & Khairia El-Said El-Nadi
Abstract

Some fraction parabolic partial differential equations driven by fraction Gaussian noise are considered. Initial-value problems for these equations are studied. Some properties of the solutions are given under suitable conditions and with Hurst parameter less than half.


2. INVERSE CAUCHY PROBLEMS FOR NONLINEAR FRACTIONAL PARABOLIC EQUATIONS IN HILBERT SPACE

by Mahmoud M. El-Borai

Abstract

This note is devoted to study an inverse Cauchy problem in a Hilbert space for fractional abstract differential equations.


3. BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON A FIXED FINITE TIME INTERVAL
by Mahmoud M.El-Borai, Khairia El-Said El-Nadi & Hoda A. Fouad
Abstract

This paper deals with a class of backward stochastic differential equations (BSDE in short) under Lipschitz and monotonicity coefficients, the authors obtain the existence and uniqueness of solution to BSDE and estimate the difference between two solutions in terms of the difference between the data (Comparison theorem).


4. A THERMOELASTIC HALF SPACE PROBLEM UNDER THE ACTION OF HEAT SOURCES AND BODY FORCES WITH TWO RELAXATION TIMES
by A.A. Abdel-Halim
Abstract

The two-dimensional problem for a half space is considered within the context of the theory of thermoelasticity with two relaxation times under the action of body forces and heat sources that permeate the medium. Laplace and exponential Fourier transform techniques are used to obtain the solution in the transformed domain by a direct approach. The inverse double transform is evaluated numerically. Numerical results are computed for the temperature, displacement and stress distributions then presented graphically.

5. AN INVESTIGATION ON FIBER OPTICAL SOLITON IN MATHEMATICAL PHYSICS AND ITS APPLICATION TO COMMUNICATION ENGINEERING
by Md. Haider Ali Biswas, Md. Ashikur Rahman & Tapasi Das
Abstract

Solitons are self-localized wave packets arising from a robust balance between dispersion and nonlinearity. Soliton is the physics of wave, acting upon wave. In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. They are a universal phenomenon, exhibiting properties typically associated with particles. Optical soliton in media with quadratic nonlinearity and frequency dispersion are theoretically analyzed. Our aim is to discuss the behavior of soliton solutions to the KdV equation and their interactions and applications are then investigated in the fiber optics solitons theory in communication engineering. In this study optical soliton is studied with illustrated graphical representation.


6. APPLICATION OF CONIC OPTIMIZATION AND SEMIDEFINITE PROGRAMMING IN CLASSIFICATION
by Abdel-Karim S.O. Hassan, Mohamed A. El-Gamal & Ahmad A.I. Ibrahim
Abstract

In this paper, Conic optimization and semidefinite programming (SDP) are utilized and applied in classification problem. Two new classification algorithms are proposed and completely described. The new algorithms are; the Voting Classifier (VC) and the N-ellipsoidal Classifier (NEC). Both are built on solving a Semidefinite Quadratic Linear (SQL) optimization problem of dimension n where n is the number of features describing each pattern in the classification problem. The voting classifier updates usage of ellipsoids in separating N different classes instead of only binary classification by using a voting unit. The N-ellipsoidal classifier makes the separation by means of N separating ellipsoids each contains one of the N learning sets of the classes intended to be separated. Experiments are performed on some data sets from UCI machine learning repository. Results are compared with several well-known classification algorithms, and the proposed approaches are shown to provide more accurate and less complex classification systems with competitive error rates.


7. A NOTE ON SMOOTH GONJUGACY OF NODE MANIFOLDS
by Fatma M. Kandil
Abstract

It was shown that there exists a unique C' smooth invariant manifold for a given dynamical system.


8. NUMERICAL ANALYSIS FOR SOME AUTONOMOUS STOCHASTIC DELAY DIFFERENTIAL EQUATIONS
by Hamdy M.Ahmed
Abstract

Numerical solution of stochastic delay differential equations is studied by using explicit one-step methods. One-step method is asymptotically zero-stable in the quadratic mean square sense.


9. POSSIBILITY OF A PHYSICAL CONNECTION BETWEEN SOLAR VARIABILITY AND GLOBAL TEMPERATURE CHANGE THROUGHOUT THE PERIOD 1970-2008
by M.A. El-Borie, A.A. Abdel-Halim, E. Shafik & S.Y. El-Monier
Abstract

The present work introduces a correlative study to investigate the possible effect of some geomagnetic and solar parameters on global surface temperature anomalies (GST). Monthly averages of GST anomalies through the period from 1970 till 2008 and four solar-geomagnetic activity indices have been used. The indices are the geomagnetic activity (aa), the sunspot number (Rz), and the dynamic pressure (nv2) throughout a period of 39 years (1970-2008) and total solar irradiance (TSI) throughout a period of 24 years (1979-2003). Scatter plots are used to show the association between GST and each of the solar-geomagnetic activity indices at zero lag. Running cross correlation analyses were applied between GST and each of these indices at different lags. Finally a series of power spectral densities (PSD) have been obtained. Our results reveal increase in GST-solar variability correlations indicated that 40-50% of this increase in GST is due to solar forcing. It is also found from correlation analysis that the change of nv2 over GST carries a phase shift of about 47 months (~4 yrs), with the change of Rz and TSI while it experiences a phase shift of 35 months (3 yrs) with the change of aa. Similarities between sets of significant peaks in the spectra of GST and solar geomagnetic activities have revealed from power spectra analyses.


10. TWO DIMENSIONAL UNSTEADY MOTION OF MICROPOLAR FLUID IN THE HALF-PLANE WHEN THE VELOCITY ARE GIVEN ON THE BOUNDARY
by Ibrahim H.Elsirafy & Aly M. Abdel-Moneim
Abstract

The object of this work is to investigate the unsteady two dimensional motion of micropolar fluid within the half-plane (-∞< x <∞, y>0 | t>0) due to the sudden motion of its horizontal boundary. Using the technique of Laplace-Fourier transform, numerical results of velocities, pressure, microrotation, stream function, stresses and moments are obtained and illustrated graphically. The classical problem of viscous fluid is included as special case and compared numerically with its analytical solution.


11. MEASUREMENT OF WELDING INDUCED DISTORTIONS IN FABRICATION OF A PROTOTYPE DRAGLINE JOINT: A CASE STUDY
by Suraj Joshi & Abdulkareem S. Aloraier
Abstract

Discontinuous welding of hollow tubular members is an important joining process in structural applications like dragline booms, cranes, pipelines, ships and bridges. The non-uniform temperature fields generated by the plume of heat energy emanating from the weld torch invariably create undesired distortions in the parent metal that negatively influence the fabrication accuracy and physical appearance. The load bearing ability and effective strength of members is further compromised by the unmitigated residual stresses that are usually left untreated owing to huge costs, long time-frames and the general infeasibility of post weld heat treatment processes. This paper presents a case study reporting the measurements of welding induced distortions in a four-member, circular hollow section tubular joint fabricated as a prototype cluster of a much larger dragline boom. Measurements were taken in a workshop setting with a coordinate measuring laser machine and were collated and analysed for predictions about the overall effect and implications of distortions. It was concluded that in welding of members of very large structures such as dragline booms, welding induced distortions produce negligible dimensional inaccuracies which could safely be left out in the overall design process.


12. ON STABILITY OF POPULATION SYSTEM
by Fatma M. Kandil
Abstract

By using the spectral properties of population operator, we investigated the existence and asymptotic behavior of the population system.


13. GAURSAT FUNCTION FOR AN ELASTIC PLATE WEAKENED BY A CURVILINEAR HOLE IN THE PRESENCE OF HEAT
by Y.A. Jaha & M.A. Abdou
Abstract

In this work, Complex Variable method is used to obtain the complex potential functions, Goursat functions, for an infinite elastic plate weakened by a curvilinear hole.


14. ADOMIAN AND BLOCK-BY-BLOCK METHODS TO SOLVE NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATION
by I.L. El-Kalla & A.M. Al-Bugami
Abstract

In this paper, the existence of a unique solution of a nonlinear two-dimensional Volterra integral equation  (NT-DVIE) with continuous kernel is discussed. Adomian Decomposition Method (ADM) and Block by block method (B by BM) are used to solve this type of NTDVIE. Numerical examples are considered to illustrate the effectiveness of the proposed methods and the error is estimated.



15. FREDHOLM-VOLTERRA INTEGRAL EQUATION WITH A GENERALIZED SINGULAR KERNEL AND ITS NUMERICAL SOLUTIONS
by I.L. El-Kalla & A.M. Al-Bugami
Abstract

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the space    L2() X C(O,T)  The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms:  Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.


16. AN INTEGRAL METHOD TO DETERMINE THE STRESS COMPONENTS OF STRETCHED INFINITE PLATE WEAKENED BY A CURVILINEAR HOLE
by M.A. Abdou & S.J. Monaquel
Abstract

An integral method, complex variable method, is used to obtain exact and closed expressions for Goursat functions for the stretched infinite plate weakened by a hole having arbitrary shape. The inner of   the infinite plate is free from stresses. The plates considered are conformally mapped on the area of the right half – plane.

The interesting cases of an infinite plate weakened by a crescent like hole or by a cut having the shape of a circular arc , also when the hole takes the form of hypotrochoidal with four round corners, are included as special cases.

17. GOURSAT FUNCTIONS OF THE THERMO-ELASTIC PROBLEM OF AN INFINITE PLATE WITH HYPITROCHOIDAL HOLE
by Ibrahim H. El-Sirafy
Abstract

Complex variable methods are used to solve the thermo-elastic problem of the infinite  isotropic homogeneous plate with a hypitrochoidal hole with multi round corners conformally mapped on the domain outside a unit circle by means of a rational mapping function .The thermo-elastic problem is equivalent to finding two analytic functions(Goursat functions)at any point  z =x + iy  within the region of the plate . The problem is transformed to solve an integrodifferential equation, in the complex plane, with singular kernel.  Closed expressions for the Goursat function and consequently the tangential thermo-elastic stresses on the boundary of the hole are obtained in quadrature in the presence of a uniform heat stream.


18. DESIGN CENTERING AND REGION APPROXIMATION USING SEMIDEFINITE PROGRAMMING
by Abdel-Karim S.O. Hassan & Ahmed Abdel-Naby
Abstract

The design centering problem seeks for the optimal values for the system designable parameters that maximize the production yield (probability of satisfying the design specifications by the manufactured systems).A new method for design centering and region approximation for a convex and bounded feasible region is introduced. The method finds iteratively a sequence of increasing-volume ellipsoids enclosing tightly selective sets of feasible points. These ellipsoids are found using semidefinite programming problem and known as Löwner-John ellipsoids. The sequence of Löwner-John ellipsoids is well definedin the method to converge to the minimum volume ellipsoid containing the feasible region. The center of the final ellipsoiddefines a design center for the proposed design problem and the ellipsoid itself is considered as a region approximation for the feasible region. Are-use of system simulations is performedin order to minimize the overall computational effort. Numerical and practical examples are considered to show the effectiveness of the new method.


19. PROJECTION-ITERATION METHOD FOR SOLVING NONLINEAR INTEGRAL EQUATION OF MIXED TYPE
by W.G. El-Sayed, M.A. Seddeek & F.M. El-Saedy
Abstract

In this paper, the existence of a unique solution of  Volterra-Hammerstein integral equation of the second kind (V-HIESK)  is proved by using Banach fixed point theorem (BFPT) in the space L2() X C[O,T]  , where  represents the domain of integration of the variable space and  is the time. Then, different kinds of projection-iteration methods (PIMs) for solving this integral equation in the space  L2() X C[O,T] are introduced. Finally, we deduced that: this method is quick convergent and the estimating error is better than the approximate error in the method of successive approximation for solving the integral equation numerically.














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